UN chief Ban Ki-moon has voiced "deep sorrow" at the death of the 23-year-old Delhi gang-rape victim, asking the Indian government to implement reforms to deter such crimes and bring the perpetrators to justice.

Ban "utterly condemns this brutal crime" and expresses "deep sorrow" at the death of the girl, who was brutally gang-raped and assaulted by six men in a moving bus in Delhi on December 16 and succumbed to her severe injuries at a Singapore hospital yesterday.

The death of the girl, whose body was cremated in Delhi this morning, led to a massive outpouring of grief and anger across India.

Millions of Indians held candle-light vigils and protests demanding immediate action from the government to punish perpetrators of the heinous crime and strengthen laws that deal with violence against women.

Ban welcomed efforts of the Indian government to take urgent action in the case and called for "further steps and reforms to deter such crimes and bring perpetrators to justice," a statement issued yesterday by the UN Secretary General's spokesperson said here.

He also encouraged the Indian government to strengthen critical services for rape victims and said the UN Women and other agencies of the United Nations stand ready to support such reform efforts with technical expertise and other support as required.

The UN chief offered his sincerest condolences to the girl's parents, family and friends.

"Violence against women must never be accepted, never excused, never tolerated. Every girl and woman has the right to be respected, valued and protected," he added.